Defuzzification is a procedure of considerable importance to control systems that use fuzzy logic because a decisive crisp output control action is required in many practical applications. Defuzzification is a strategy for reaching a final and crisp control decision for a fuzzy logic control system. Various strategies have been advanced including the center of area (COA) and mean of maximum (MOM) approaches.
In an earlier paper, published in EEE Transactions on Fuzzy Systems, Vol. 4, No. Feb. 1, 1996, we have proposed two compromise strategies that combine these two methods, a Gaussian distribution transformation-based defuzzification (GTD) and a polynomial transformation-based defuzzification (PTD). Both strategies can perform better than existing strategies and include the COA and MOM strategies as special cases. Both are based on parameter learning processes using a Kalman filter 50 as to provide iterative improvement algorithms on sample database containing fuzzy sets and the associated defuzzied values. The PTD strategy particularly offers a generalized defuzzification tool for a wide class of possible problems. In particular, this defuzzification strategy does not use a Gaussian function as a specific transformation model as is characteristic of GTD for the weighting function used in the decision making process. Instead, it models the transformation as a polynomial expansion. However, the parameter learning processes are the keys to success in applying either of these strategies. Although various learning models are available, we chose the extended Kalman filter for this role.
As is mentioned in our paper, the strategies discussed were single-mode oriented, where only a single peak in the membership function may exist, but in multi-mode situations where two or more distinct peaks in the membership distribution may occur, the above strategies may lead to inappropriate conclusions.
An object of the present invention is to modify our original PTD strategy to better handle multi-mode situations.